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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Differential Geometry (MATH11235)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 5 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis course is an introduction to differentiable manifolds from an intrinsic point of view, leading to classical theorems such as the generalised Stokes' theorem. It extends the subject matter of Y3 Geometry from surfaces (embedded in R^3) to differentiable manifolds of arbitrary dimension (not necessarily embedded in another space). This provides the necessary concepts to start studying more advanced areas of geometry, topology, analysis and mathematical physics.
Course description The course will include the following topics:
- Smooth manifolds, the manifold topology and submanifolds as level sets
- Tangent and cotangent spaces, derivative of a smooth map.
- Tangent bundle, vector fields, derivations, flows, Lie derivative.
- Vector bundles, tensor fields.
- Differential forms, Cartan calculus, de Rham complex.
- Orientation, integration, Stokes's theorem.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Algebra (MATH10069) AND Geometry (MATH10074)
Prohibited Combinations Students MUST NOT also be taking
Other requirements Students MUST have not taken Differentiable Manifolds (MATH10088)
Information for Visiting Students
Pre-requisitesVisiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling
High Demand Course? Yes
Course Delivery Information
Academic year 2022/23, Available to all students (SV1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 20%, Examination 80%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)Differential Geometry (MATH11235)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Explain the concept of a manifold and give examples
  2. Perform coordinate-based and coordinate-free calculations on manifolds
  3. Describe vector fields from different points of view and indicate the links between them
  4. Work effectively with tensor fields and differential forms on manifolds
  5. State and use Stokes' theorem
Reading List
Recommended in addition to materials provided:
(*)John Lee, Introduction to smooth manifolds, Springer 2012
Michael Spivak, Calculus on manifolds, Benjamin, 1965
Theodor Broecker & Klaus Jaenich, Introduction to Differential Topology, CUP 1982
(*)Loring Tu, Introduction to Manifolds, Springer 2010
(*) are available to download from the University Library
Additional Information
Graduate Attributes and Skills Not entered
KeywordsDG,Differential geometry,smooth manifolds
Course organiserProf José Figueroa-O'Farrill
Tel: (0131 6)50 5066
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
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